Mathematical Foundations of Quantum Mechanics (theoretical physics Book 1)

Understanding quantum mechanics means first and foremost understanding its mathematical structure: this is the premise behind this book. Not a traditional textbook nor a collection of applications, but a journey that builds the formal language of the theory, freeing it from the perception of a set of mysterious rules. The treatment develops in an organic manner the fundamental tools: complex numbers, differential and integral calculus, differential equations and eigenvalue problems; linear algebra in complex vector spaces, linear operators and unitary diagonalization; Hilbert spaces, Dirac notation, commutators, Fourier transforms, and probabilistic structure. Organized into five progressive parts, the book guides the reader step by step, revealing the unity of the formalism, with exercises at three levels and sections devoted to the most common mistakes, for a solid and informed understanding of the theory. Read more